Analysis of residual interference after MSE linear equalization of multitone spread spectrum signals

The combination of multitone modulation with direct sequence spectrum spreading has been introduced by Vandendorpe (see IEEE International Zurich Seminar, p.440-451, 1994). The performance of a correlation receiver has been evaluated for a multipath channel. The analysis has been extended to the presence of a multiple access interference. We analyze the equalization problem of such a system. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method.